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Use logarithms to solve the equation 2^(5x) = 3^(2x+1) , giving the answer correct to 3 significant figures

Taking the log of both sides we get 5x * ln2 = (2x+1) * ln3.
Taking everything that contains x to the left side: x * (5ln2 - 2ln3) = ln3.
Therefore x=ln3/(5ln2 - 2ln3)
x is approx 0.866

Answered by Beatrice B. • Maths tutor

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Use logarithms to solve the equation 2^(5x) = 3^(2x+1) , giving the answer correct to 3 significant figures

Related Maths A Level answers

Use the addition formulas: sin(x+y)=sin(x)*cos(y)+sin(y)*cos(x), cos(x+y)=cos(x)*cos(y)-sin(x)*sin(y) to derive sin(2x), cos(2x), sin(x)+sin(y).

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